AtlasUnified/atlas-math-sets-2.5

Atlas Math 2.5

Atlas Math 2.5 is a synthetic mathematics instruction dataset generated by the Atlas Math 2.5 codebase. It updates the Atlas Math 2.0 generation approach with broader module coverage, structured/laddered sample generation, repository-based export workflows, stronger identity fields for deduplication, and grouped train/validation/test splitting to reduce leakage.

The dataset is designed for math instruction following, answer generation, and step-oriented mathematical reasoning. It is not intended to be a benchmark of human-authored contest solutions.

Dataset summary

Atlas Math 2.5 contains generated English math prompts across multiple K-12 and early undergraduate math areas. Each row pairs an instruction and math problem with an answer. Rich exports also include topic, subtopic, difficulty, module identity, canonical keys, case identifiers, family identifiers, template identifiers, split grouping keys, and validation metadata.

Core topic coverage in the current generator bundle:

Topic	Registered modules
algebra	32
arithmetic	20
calculus	22
geometry	20
prealgebra	20
precalculus	25
trigonometry	13

Total registered modules: 152.

Intended use

Suitable uses:

• Instruction-tuning math assistants.
• Evaluating synthetic data generation pipelines.
• Training models to answer structured math questions.
• Curriculum-style data mixing by difficulty level.
• Dataset filtering, deduplication, and split-leakage experiments.

Unsuitable uses:

• High-stakes grading without independent validation.
• Claims of complete mathematical coverage.
• Treating every generated answer as human-verified.
• Benchmarking frontier mathematical reasoning without contamination controls.

Data format

The recommended Hugging Face export format is JSONL with the following fields.

Default hf format

{
  "prompt": "Solve the equation step by step:\n\n3x + 5 = 20",
  "response": "x = 5",
  "instruction": "Solve the equation step by step:",
  "input": "3x + 5 = 20",
  "answer": "x = 5",
  "difficulty": "level_1",
  "topic": "algebra",
  "subtopic": "linear_equations",
  "module_id": "algebra.linear_equations_single_variable",
  "generator": "structured",
  "sample_id": "...",
  "case_id": "...",
  "canonical_key": "...",
  "family_id": "...",
  "template_id": "...",
  "split_group_key": "...",
  "validation": {
    "is_valid": true,
    "errors": []
  }
}

Alternate formats

The exporter can also render:

• chatml: messages=[{"role":"user",...},{"role":"assistant",...}]
• alpaca: instruction, input, output

Splits

Recommended split policy:

• train: 90%
• validation: 5%
• test: 5%
• split mode: grouped_canonical
• seed: 42

Grouped splitting should be preferred over random splitting because generated samples may share templates, canonical forms, or parameter families. Use the leakage_audit section of dataset_dict.json to check whether canonical_key, case_id, or family_id values appear across multiple splits.

Generation workflow

Typical workflow from the code repository:

# Inspect registered generators
python -m atlas_math.cli list --json

# Build raw generated records directly
python -m atlas_math.cli build \
  --target-records 20000 \
  --difficulty-mix balanced \
  --format rich \
  --dedupe-mode input_answer \
  --workers 1 \
  --output outputs/atlas_math_25_raw.jsonl

# Export a repository of module-level samples/cases
python -m atlas_math.cli repository \
  --output-dir repository \
  --samples-per-level 50 \
  --cases-per-level 500 \
  --format rich

# Build a curated repository-derived JSONL
python -m atlas_math.cli repository-build \
  --repository-dir repository \
  --target-records 20000 \
  --difficulty-mix balanced \
  --dedupe-mode input_answer \
  --source-kind auto \
  --output outputs/atlas_math_25.jsonl

The interactive CLI also includes an HF export action that writes train.jsonl, validation.jsonl, test.jsonl, and dataset_dict.json.

Quality controls

The generator includes these controls:

• post-hoc deduplication modes:
  • input_answer
  • input_only
  • full
  • canonical
  • case_id
  • family
• identity fields:
  • sample_id
  • case_id
  • canonical_key
  • family_id
  • template_id
  • split_group_key
• split modes:
  • random
  • grouped_canonical
  • grouped_case
  • grouped_family
• validation metadata on repository-built rows.
• repository coverage reports and dashboards.

Known limitations

• The data is synthetic and may contain generated math errors.
• Some modules use template families with limited variation.
• Difficulty labels are generator-defined and should not be treated as standardized grade levels.
• Generated explanations or step-oriented answers may be concise and should not be assumed to contain full formal proofs.
• Before publication, run a module-level smoke test and inspect validation summaries for invalid rows, duplicates, and split leakage.

Recommended publication checklist

Before uploading a release:

1. Run python -m compileall atlas_math.
2. Run python -m atlas_math.cli list --json.
3. Smoke-test each registered module at least once.
4. Generate a repository export.
5. Export HF splits.
6. Inspect dataset_dict.json.
7. Confirm all split-leakage audit values are empty or explain expected overlaps.
8. Spot-check at least 100 random examples across topics and difficulty levels.
9. Confirm the repository includes README.md, LICENSE, pyproject.toml, and a minimal test suite.
10. Pin the exact code commit used to generate the dataset.

Citation

@misc{atlasmath25,
  title = {Atlas Math 2.5},
  author = {AtlasUnified},
  year = {2026},
  howpublished = {Synthetic mathematics instruction dataset and generator},
  url = {https://github.com/atlasunified/atlas-math-v2.5}
}

License

MIT.